What is the slope of a line that is perpendicular to the line shown on the graph?
-4
1 1/4
1/4
4
Answer (2)
The problem requires finding the slope of a line perpendicular to a line with a slope of -4.
Perpendicular lines have slopes that are negative reciprocals of each other.
Calculate the negative reciprocal of -4: − − 4 1 = 4 1 .
The slope of the perpendicular line is 4 1 .
Explanation
Understanding the Problem The problem asks us to find the slope of a line that is perpendicular to a given line. We are given that the slope of the original line is -4.
Key Concept: Perpendicular Lines The key concept here is that perpendicular lines have slopes that are negative reciprocals of each other. This means that if one line has a slope of m , a line perpendicular to it will have a slope of − m 1 .
Applying the Concept In our case, the given line has a slope of m 1 = − 4 . To find the slope of a line perpendicular to it, we need to calculate the negative reciprocal of -4.
Calculating the Slope The negative reciprocal of -4 is calculated as follows: m 2 = − m 1 1 = − − 4 1 = 4 1 So, the slope of the perpendicular line is 4 1 .
Final Answer Therefore, the slope of a line perpendicular to the given line with a slope of -4 is 4 1 .
Examples
Imagine you're designing a rectangular garden. If one side of the garden needs to have a slope of -4 (meaning it descends steeply), and you want the adjacent side to be perfectly level (perpendicular), the level side needs to have a slope that is the negative reciprocal of -4, which is 4 1 . This ensures the sides meet at a right angle, creating a well-defined rectangular shape. Understanding perpendicular slopes is crucial in various fields like architecture, construction, and even creating accurate maps.
The slope of a line that is perpendicular to a line with a slope of -4 is 4 1 . This result comes from calculating the negative reciprocal of the original slope. Therefore, the correct choice is 4 1 .
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